Problem: Reduce to lowest terms: $ \dfrac{7}{4} \div - \dfrac{3}{4} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{4}$ is $- \dfrac{4}{3}$ Therefore: $ \dfrac{7}{4} \div - \dfrac{3}{4} = \dfrac{7}{4} \times - \dfrac{4}{3} $ $ \phantom{ \dfrac{7}{4} \times - \dfrac{4}{3}} = \dfrac{7 \times -4}{4 \times 3} $ $ \phantom{ \dfrac{7}{4} \times - \dfrac{4}{3}} = \dfrac{-28}{12} $ The numerator and denominator have a common divisor of $4$, so we can simplify: $ \dfrac{-28}{12} = \dfrac{-28 \div 4}{12 \div 4} = -\dfrac{7}{3} $